# How do you find the derivative of g(t) = 1/t^(1/2)?

Mar 1, 2017

$g ' \left(t\right) = - \frac{1}{2 {t}^{\frac{3}{2}}}$

#### Explanation:

$g \left(t\right) = \frac{1}{t} ^ \left(\frac{1}{2}\right) = {t}^{- \frac{1}{2}}$

Applying the power rule:

$g ' \left(t\right) = - \frac{1}{2} {t}^{\left(- \frac{1}{2} - 1\right)} = - \frac{1}{2} {t}^{- \frac{3}{2}}$

$= - \frac{1}{2 {t}^{\frac{3}{2}}}$